We now turn to rank 3 sheaves, with \(\gamma =[3,-1,2-n)\) , discriminant \(\Delta =\frac{n}{3}-\frac{1}{9}\) .
The condition (REF )
gives \(\Delta \ge \delta _{\rm LP}(-\frac{1}{3})=\frac{5}{9}\)  for non-exceptional sheaves.
The generating function is given by [1]} [2]}
\(\begin{aligned}h_{3,-1} &= (y+1+1/y^2) q^2 + (y^8+2y^6+5y^4+8y^2+10+\dots ) q^3 + \dots \\&\rightarrow 3q^2 + 42 q^3 + 333 q^4 + 1968 q^5 + 9609 q^6+ \dots \end{aligned}\) 
